Be aware that paired t-test is a parametric assessment. The distribution of differences is normally distributed. There should be no extreme outliers in the differences. We calculate the difference in exam scores for each student. The second variable is a measurement. Types of t-tests. Paired Samples t-test: Example PROC TTEST includes QQ plots for the differences between day 1 and day 3. The paired t-test, also referred to as the paired-samples t-test or dependent t-test, is used to determine whether the mean of a dependent variable (e.g., weight, anxiety level, salary, reaction time, etc.) Visit the individual pages for each type of t-test for examples along with details on assumptions and calculations. Build practical skills in using data to solve problems better. For each person, we have the weight at the start and end of the program. This can be evaluated by comparing the result of the t-test with and without the outlier. Also, the distribution of differences between the paired measurements should be normally distributed. In the Shapiro and Levene’s test, a non-significant result is good and indicates that the assumptions of the paired sample t-test or repeated measures ANOVA are met. If the population from which paired differences to be analyzed by a paired t test were sampled violate one or more of the paired t test assumptions, the results of the analysis may be incorrect or misleading. Calculation: The assumptions that you have to analyze when deciding the kind of test you have to implement are: Paired or unpaired: The data of both groups come from the same participants or not. Data contains paired samples . T-Test Essentials: Definition, Formula and Calculation. For the results of a paired samples t-test to be valid, the following assumptions should be met: The participants should be selected randomly from the population. The dependent t-test (called the paired-samples t-test in SPSS Statistics) compares the means between two related groups on the same continuous, dependent variable. The figure below shows results for the paired t-test for the exam score data using JMP. The mean differences should be normally distributed. Is this “close enough” to zero for the instructor to decide that the two exams are equally difficult? The dependent variable is measured on an incremental level, such as ratios or intervals. From the statistics, we see that the average, or mean, difference is 1.3. ... (2 measurements from the same group of subjects) then you should use a Paired Samples T-Test instead. She wants to know if the exams are equally difficult and wants to check this by looking at the differences between scores. Each of the paired measurements must be obtained from the same subject. Enough Data. Assumptions for an Independent Samples T-Test. (Note that the statistics are rounded to two decimal places below. This also referred as the two sample t test assumptions.. In such situations, paired t-test can be used to compare the mean weights before and after treatment. There are a few assumptions that the data has to pass before performing a paired t-test in SPSS. This chapter describes the different types of t-test, including: one-sample t-tests, independent samples t-tests: Student’s t-test and Welch’s t-test; paired samples t-test. SPSS reports the mean and standard deviation of the difference scores for each pair of variables. The alternative is two-tailed and alpha = .05. From the histogram, we see that there are no very unusual points, or outliers. This also referred as: The procedure of the paired t-test analysis is as follow: The paired samples t-test assume the following characteristics about the data: In this section, we’ll perform some preliminary tests to check whether these assumptions are met. You can use the test when your data values are paired measurements. We compare the value of our statistic (0.750) to the. The formula to calculate the t-statistic for a paired t-test is: where, t = t-statistic; m = mean of the group; µ = theoretical value or population mean; s = standard deviation of the group Here are three examples: To apply the paired t-test to test for differences between paired measurements, the following assumptions need to hold: An instructor wants to use two exams in her classes next year. We cannot reject the hypothesis of a normal distribution. Before jumping into the analysis, we should plot the data. Measurements for one subject do not affect measurements for any other subject. The software shows a p-value of 0.4650 for the two-sided test. Here is the data: If you look at the table above, you see that some of the score differences are positive and some are negative. The formula shows the sample standard deviation of the differences as sd and the sample size as n. $t = \frac{\mathrm{\mu_d}}{\frac{s}{\sqrt{n}}}$. 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